why is 00000000 - 00000001 = 11111111 in C unsigned char data type?

Question

I observed that, when a unsigned char variable stores the value 0 (00000000₂) and it gets decremented by 1 (00000001₂), the variable value turns into 255 (11111111₂), which is the highest value that a unsigned char variable can hold.

My question is: why 00000000₂ - 00000001₂ turns into 11111111₂? (I want to see the arithmetic behind it)

The C code in which i observed it was this one:

#include <stdio.h>

main(){

  unsigned char c = 0;

  unsigned char d = c - 1;

  printf("%d\n%d", c, d);

}

When it runs, the following output is shown:

0
255

Answer 1

See here:

Unsigned integer arithmetic is always performed modulo 2ⁿ where n is the number of bits in that particular integer. E.g. for unsigned int, adding one to UINT_MAX gives ​0​, and subtracting one from ​0​ gives UINT_MAX.

So in your example, since unsigned char is usually 8 bit, you get 2⁸-1 = 255.